SOLUTION: Please help me on this problem Mang Jose wants to enclose a rectangular lot beside a river with 120 meters of barbed wire. The side along the river will not need fencing. a.

Question 158702: Please help me on this problem
Mang Jose wants to enclose a rectangular lot beside a river with 120 meters of barbed wire. The side along the river will not need fencing.
a. Express the lot area in terms of its length.
b. Construct a table of values and test if the relation is quadratic or not.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mang Jose wants to enclose a rectangular lot beside a river with 120 meters of barbed wire. The side along the river will not need fencing.
:
a. Express the lot area in terms of its length.
:
Let x = the length of the rectangular area;
Let w = the width
:
120 meters of fence will be used to enclose 3 sides. (only one length required)
x + 2w = 120
2w = (120-x)
Divide equation by 2
w =
w = (60-.5x)
:
Area = x * w
Substitute (60-.5x) for w
A = x(60-.5x)
A = 60x - .5x^2; (area in terms of the length)
:
:
b. Construct a table of values and test if the relation is quadratic or not.
Choose some convenient values (y = area)
x | y
-------
10 |550; 600 - .5(10^2)
20 |1000
60 |1800
100|1000; note it reached a max, and decreased, it's a quadratic (and it has an x^2)
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